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<p>The emergence of a widespread infectious disease led to a global health crisis, profound disruptions to health systems, societies, and economies. This study introduces a nonlinear and bilinear incidence function into the infection process within the dynamical system. We develop and analyze an epidemic model structured into compartments for susceptible, exposed, asymptomatic, symptomatic, and recovered individuals. The model is rigorously examined to confirm solution non-negativity and boundedness, identifying disease-free and endemic equilibrium points. The basic reproduction number is derived, followed by stability, sensitivity, and bifurcation analyses to evaluate the influence of key parameters. Model parameters are estimated using real data from four countries to validate the proposed framework. Moreover, an optimal control framework is formulated to limit infection spread, incorporating vaccination of susceptible individuals <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(u_1(t)\)</EquationSource> </InlineEquation> and healthcare support <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(u_2(t)\)</EquationSource> </InlineEquation> applied to both asymptomatic and symptomatic infected populations.</p>

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Infection dynamics and control strategies in a nonlinear epidemic model

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月30日

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  • G. Swathi,
  • G. S. Mahapatra,
  • R. Prem Kumar

摘要

The emergence of a widespread infectious disease led to a global health crisis, profound disruptions to health systems, societies, and economies. This study introduces a nonlinear and bilinear incidence function into the infection process within the dynamical system. We develop and analyze an epidemic model structured into compartments for susceptible, exposed, asymptomatic, symptomatic, and recovered individuals. The model is rigorously examined to confirm solution non-negativity and boundedness, identifying disease-free and endemic equilibrium points. The basic reproduction number is derived, followed by stability, sensitivity, and bifurcation analyses to evaluate the influence of key parameters. Model parameters are estimated using real data from four countries to validate the proposed framework. Moreover, an optimal control framework is formulated to limit infection spread, incorporating vaccination of susceptible individuals \(u_1(t)\) and healthcare support \(u_2(t)\) applied to both asymptomatic and symptomatic infected populations.